%I #17 Aug 12 2012 18:57:30
%S 1,1,1,2,1,3,2,3,1,4,3,3,2,2,3,4,1,5,4,4,3,5,3,3,2,2,2,5,3,3,4,5,1,6,
%T 5,5,4,4,4,4,3,3,5,5,3,6,3,3,2,2,2,6,2,2,5,5,3,3,3,3,4,4,5,6,1,7,6,6,
%U 5,5,5,5,4,7,4,4,4,4,4,4,3,3,3,3,5,7,5,5,3,3,6
%N Length of longest palindromic prefix of (n base 2).
%C Since the binary expansion of n always begins with a 1, a final 0 can't affect the result, so a(2n) = a(n).
%H N. J. A. Sloane, <a href="/A215467/b215467.txt">Table of n, a(n) for n = 0..10000</a>
%e ...
%e 4 = 100 -> 1
%e 5 = 101 -> 3
%e 6 = 110 -> 2
%e 7 = 111 -> 3
%e 8 = 1000 -> 1
%e 9 = 1001 -> 4
%e ...
%p rev := proc(lis)
%p local t1,n,i;
%p t1:=[]; n:=nops(lis);
%p for i from 1 to n do t1:=[op(t1),lis[n+1-i]]; end do;
%p return t1;
%p end proc;
%p isPal := proc(L)
%p local d ;
%p for d from 1 to nops(L)/2 do
%p if op(d, L) <> op(-d, L) then
%p return false;
%p end if;
%p end do:
%p return true;
%p end proc:
%p A215467L := proc(L)
%p local a, c;
%p a := 1 ;
%p for c from 2 to nops(L) do
%p if isPal( [op(1..c, L)] ) then
%p a := c ;
%p end if;
%p end do:
%p return a;
%p end proc:
%p A215467 := proc(n)
%p if n <= 1 then 1;
%p else rev(convert(n, base, 2)) ;
%p A215467L(%) ;
%p end if;
%p end proc:
%Y Cf. A050430, A215469.
%K nonn,base
%O 0,4
%A _N. J. A. Sloane_, Aug 11 2012